Quasi-Frobenius Rings and Nakayama Permutations of Semiperfect Rings
We say that \(A \) is a ring with duality for simple modules, or simply a DSM-ring, if, for every simple right (left) \(A \) -module U, the dual module U* is a simple left (right) \(A \) -module. We prove that a semiperfect ring is a DSM-ring if and only if it admits a Nakayama permutation. We introduce the notion of a monomial ideal of a semiperfect ring and study the structure of hereditary semiperfect rings with monomial ideals. We consider perfect rings with monomial socles., number=7, journal=Ukrains’kyi Matematychnyi Zhurnal, author=Dokuchaev, M. A. and Kirichenko, V. V., year=2002, month=Jul., pages=919–930